In mathematics, the Freudenthal magic square (or Freudenthal–Tits magic square) is a construction relating several Lie algebras (and their associated Lie groups). It is named after Hans Freudenthal and Jacques Tits, who developed the idea independently. It associates a Lie algebra to a pair of division algebras A, B. The resulting Lie algebras have Dynkin diagrams according to the table at the right. The "magic" of the Freudenthal magic square is that the constructed Lie algebra is symmetric in A and B, despite the original construction not being symmetric, though Vinberg's symmetric method gives a symmetric construction.
The Freudenthal magic square includes all of the exceptional Lie groups apart from G2, and it provides one possible approach to justify the assertion that "the exceptional Lie groups all exist because of the octonions": G2 itself is the automorphism group of the octonions (also, it is in many ways like a classical Lie group because it is the stabilizer of a generic 3-form on a 7-dimensional vector space – see prehomogeneous vector space).
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In mathematics, the Freudenthalmagicsquare (or Freudenthal–Tits magicsquare) is a construction relating several Lie algebras (and their associated Lie...
design Freudenthalmagicsquare John R. Hendricks Hexagonal tortoise problem Latin squareMagic circle Magic cube classes Magic polygon Magic series Most-perfect...
basis of stable homotopy theory. The Freudenthalmagicsquare is a construction in Lie algebra developed by Freudenthal (and independently by Jacques Tits)...
structure algebras also form part of Tits' construction of the Freudenthalmagicsquare. A (possibly nonassociative) algebra over the real numbers is said...
algebras) and Susumu Okubo (Okubo algebras) and others.: 463–81 Freudenthalmagicsquare Pfister form Triality Wikibooks has a book on the topic of: Associative...
Riemannian symmetric spaces, both compact and non-compact, via a Freudenthalmagicsquare construction. The irreducible compact Riemannian symmetric spaces...
octonionic number theory, and concludes with a chapter on the Freudenthalmagicsquare and related constructions. Although presented at an undergraduate...
of H give the complexifications of the first three rows of the Freudenthalmagicsquare. Other Hermitian symmetric spaces yields prehomogeneous vector...
Zelmanov tackled the remaining cases involving the Freudenthalmagicsquare and extended this square to exceptional Lie superalgebras. Later Benkart extended...
index Tits metric Tits systems Bruhat–Tits fixed point theorem Freudenthal–Tits magicsquare Kantor–Koecher–Tits construction Artin-Tits group Kneser–Tits...
(1994). "Uniform tilings of 3-space". Geombinatorics. 4 (2): 49–56. Freudenthal, H; van der Waerden, B. L. (1947), "Over een bewering van Euclides ("On...
The Smurf movie on February 14, 2025, The SpongeBob Movie: Search for SquarePants on December 19, 2025, Plankton: The Movie in 2025, Aang: The Last Airbender...
statewide election in Wyoming was in 2006, when Democratic governor Dave Freudenthal was re-elected to a second term by a wide margin, winning every county...
Combination Ruben Fleischer†♦ – Zombieland Tom Ford – A Single Man Thor Freudenthal† – Hotel for Dogs Cary Joji Fukunaga† – Sin Nombre Ricky Gervais♦ – The...
4 smartphone is introduced. October 10 – My Little Pony: Friendship is Magic debuts on the Hub. The same day that Discovery Kids was relaunched as The...
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